English

Compactly generated t-structures in the derived category of a commutative ring

Commutative Algebra 2018-08-08 v3 K-Theory and Homology

Abstract

We classify all compactly generated t-structures in the unbounded derived category of an arbitrary commutative ring, generalizing the result of [ATLJS10] for noetherian rings. More specifically, we establish a bijective correspondence between the compactly generated t-structures and infinite filtrations of the Zariski spectrum by Thomason subsets. Moreover, we show that in the case of a commutative noetherian ring, any bounded below homotopically smashing t-structure is compactly generated. As a consequence, all cosilting complexes are classified up to equivalence.

Keywords

Cite

@article{arxiv.1806.00078,
  title  = {Compactly generated t-structures in the derived category of a commutative ring},
  author = {Michal Hrbek},
  journal= {arXiv preprint arXiv:1806.00078},
  year   = {2018}
}

Comments

26 pages. Corrected an error from the previous version, resulting in reformulation of the main results, and a new section

R2 v1 2026-06-23T02:15:20.882Z